Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21077 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,35)(27,39)(28,33)(29,44)(30,34)(31,37)(32,42)(36,50)(38,46)(40,54)(41,48)(43,47)(45,55)(49,52)(51,53);(20,22,23,21)(24,26,29,37,30,38,28,43)(25,31,33,35,34,47,44,46)(27,36,41,51,42,52,40,55)(32,45,48,49,39,53,54,50);(24,27,29,41,30,42,28,40)(25,32,33,48,34,39,44,54)(26,36,37,51,38,52,43,55)(31,45,35,49,47,53,46,50);(24,28,30,29)(25,33,34,44)(26,37,38,43)(27,40,42,41)(31,46,47,35)(32,48,39,54)(36,51,52,55)(45,50,53,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14065);